THINGS TO TRY

SNAPSHOTS

DETAILS

The parametric equation of a circular cylinder with radius inclined at an angle from the vertical is:

, with parameters and .

Define the functions and . The and functions define the composite curve of the -gonal cross section of the polygonal cylinder [1].

The parametric equation of a polygonal cylinder with sides and radius rotated by an angle around its axis is:

with parameters and .

To find the equation of the intersection curve, put . This gives the three equations:

,

,

.

These are equations with four variables, , , , and . Eliminating , , and by solving the equations gives the parametric curve of the intersection with θ as the only parameter (choosing gives the upper or lower half of the intersection curve):